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Factor Analysis

Factor Analysis. Revealing the correlational structure among variables Understanding & Reducing Complexity. Some Uses of Factor Analysis. Understand association among constructs – structure of correlations (what are main dimensions that underlie the set of constructs?)

virginia-ramirez
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Factor Analysis

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  1. Factor Analysis Revealing the correlational structure among variables Understanding & Reducing Complexity

  2. Some Uses of Factor Analysis • Understand association among constructs – structure of correlations (what are main dimensions that underlie the set of constructs?) • Scale construction (which test items go together? How many constructs are being measured?) • Data reduction (which variables can be combined together). For example, precursor to MANOVA • As part of Full Structural Equation Modeling / Latent Variable Analysis

  3. Two forms of factor analysis • Exploratory • Let the data indicate what’s going on, with no (or little) expectations • Confirmatory • Evaluate a specific, clearly-articulated hypotheses about a correlational structure among variables • Get “fit” indices & significance tests

  4. An intuitive overview of Exploratory Factor Analysis • Consider these eight personality attributes: • Assertive • Talkative • Thoughtful • Intellectual • Dominant • Influential • Creative • Imaginative • Is there redundancy? • Can we reduce these eight concepts to more basic dimensions?

  5. An intuitive overview of Factor Analysis • Ask people to rate themselves on each term (How X are you on a 1 to 10 scale)? • 2) Compute correlations among the terms. – Do people who score high on one attribute score high on the other?

  6. Factor Analysis Correlation Matrix

  7. Factor Analysis • Step 3) Interpret the pattern of correlations – what is related to what? • Step 4) Identify clusters of items? “Factors” • Step 5) Psychologize – name the factors – what are the underlying dimensions?

  8. Three Core Questions in Exploratory FA • Number of factors/dimensions • How many factors are there? • Do the variables have a one-factor correlational structure, two-factor, etc? • Eigenvalues, “scree” plot • Interpretability of factor meanings (see next question)

  9. Three Core Questions in Exploratory FA • Number of factors/dimensions • What are the factors – psychological meaning? • The meaning of a factor emerges from the nature of the variables that “load” on it • Which vbls “load” most strongly on which factors? • Loadings (-1 to +1, more or less). More extreme = variable is more strongly associated with factor

  10. Three Core Questions in Exploratory FA • Number of factors/dimensions • What are the factors – psychological meaning? • Factor-factor associations (if more than 1 factor) • Are the factors correlated with each other? • Are there “superfactors”? • The answer may depend on “rotation” method

  11. Doing a “real” factor analysis:SPSS and Affect • Steps in the analysis • Are you doing a factor analysis or a principle components analysis? • “Extraction method” • Often there’s little practical difference • Decide how many factors to examine (extract) • Again, based on “scree” plot, interpretability • Decide whether to “rotate” the factors (generally done) • Clarifies the results • Which type of rotation to use? • Orthogonal (eg Varimax) or Oblique (eg, Promax) • Implications for correlations among factors • 4. Examine the rotated factor/component matrix • Interpret the factor loadings to interpret the meaning of the factors • NOTE – this is sometimes a back-and-forth process

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